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Article Dans Une Revue Graphs and Combinatorics Année : 2020

Ear-Slicing for Matchings in Hypergraphs

András Sebő
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Résumé

We study when a given edge of a factor-critical graph is contained in a matching avoiding exactly one, pregiven vertex of the graph. We then apply the results to always partition the vertex-set of a $3$-regular, $3$-uniform hypergraph into at most one triangle (hyperedge of size $3$) and edges (subsets of size $2$ of hyperedges), corresponding to the intuition, and providing new insight to triangle and edge packings of Cornu\'ejols' and Pulleyblank's. The existence of such a packing can be considered to be a hypergraph variant of Petersen's theorem on perfect matchings, and leads to a simple proof for a sharpening of Lu's theorem on antifactors of graphs.

Dates et versions

hal-02860412 , version 1 (08-06-2020)

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András Sebő. Ear-Slicing for Matchings in Hypergraphs. Graphs and Combinatorics, 2020, 36, pp.1947 - 1951. ⟨10.1007/s00373-020-02228-y⟩. ⟨hal-02860412⟩
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